arXiv subjects

Huixuan Wu

Publications and source records attributed to Huixuan Wu.

3 recordsLinked to original sources

arXiv2026

Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm

Reconstructing fields governed by nonlinear partial differential equations (PDEs) from sparse measurements is a challenging task because the governing equations are strongly nonlinear and observations are available at only a few locations. Fluid velocity fields are a representative case. In this paper, we propose a variational quantum algorithm that reconstructs the solution over the entire spacetime domain at once. Rather than marching in time, the method encodes the full discrete spacetime solution in a single variational quantum state, so that all time points are optimized jointly. The cost function combines a sparse-measurement mismatch term with a physics-informed PDE violation term, letting data and the governing equation constrain the solution simultaneously. We demonstrate the method on the one-dimensional Burgers and Kuramoto--Sivashinsky equations using numerical simulations. The results suggest that variational quantum algorithms with a spacetime encoding scheme offer a compact framework for reconstructing nonlinear PDE dynamics.

quant-ph↗

arXiv2026

Efficient Quantum Simulation of Variable-Coefficient Transport with Continuous Source Injection

Quantum time-marching algorithms for transport PDEs often represent variable coefficients and forcing through register-expanding dilations, block-encoding oracles, or repeated postselection. We present an alternative algorithm for a forced variable-coefficient advection-diffusion equation in flow-inspired skew-symmetric form that incorporates spatially varying velocity, viscous dissipation, and persistent source injection with a peak logical requirement of $n_q+1$ qubits. A centered skew-symmetric discretization makes the advection operator strictly skew-Hermitian for arbitrary velocity profiles, enabling an ancilla-free unitary realization using a Gray-code Trotter sequence of controlled-$R_y$ rotations. Diffusion is applied in the Fourier basis through a uniformly controlled rotation on one postselected ancilla, which is measured, reset, and reused between the two diffusion half-steps, while the source is incorporated classically through second-order Strang splitting. Statevector simulations for $N=16$ and $32$ recover second-order temporal convergence against high-accuracy classical solutions, while Richardson extrapolation gives fourth-order accuracy and reduces kernel calls by factors of four to fourteen. Independent tests through $N=256$ confirm second-order spatial consistency. We further show that the per-step ancilla failure probability is proportional to the instantaneous viscous dissipation rate, making postselection cost self-regulating over a fifty-fold viscosity range. Stable evolution is demonstrated for $5\times10^4$ time steps without observable secular error growth, while Gray-code advection accounts for $71$--$95\%$ of transpiled controlled-NOT gates. The fixed-width kernel provides a qubit-efficient building block for near-term hardware studies, although classical readout and state re-preparation remain the main obstacles to coherent multistep evolution.

quant-ph↗

arXiv2024

Beyond Point Annotation: A Weakly Supervised Network Guided by Multi-Level Labels Generated from Four-Point Annotation for Thyroid Nodule Segmentation in Ultrasound Image

Weakly-supervised methods typically guided the pixel-wise training by comparing the predictions to single-level labels containing diverse segmentation-related information at once, but struggled to represent delicate feature differences between nodule and background regions and confused incorrect information, resulting in underfitting or overfitting in the segmentation predictions. In this work, we propose a weakly-supervised network that generates multi-level labels from four-point annotation to refine diverse constraints for delicate nodule segmentation. The Distance-Similarity Fusion Prior referring to the points annotations filters out information irrelevant to nodules. The bounding box and pure foreground/background labels, generated from the point annotation, guarantee the rationality of the prediction in the arrangement of target localization and the spatial distribution of target/background regions, respectively. Our proposed network outperforms existing weakly-supervised methods on two public datasets with respect to the accuracy and robustness, improving the applicability of deep-learning based segmentation in the clinical practice of thyroid nodule diagnosis.

eess.IV↗